Distribution-guided heuristic search for nonlinear parameter estimation with an application in semiconductor manufacturing

Abstract

Estimating a batch of parameter vectors of a nonlinear model is considered, where there exists a model interpreting the independent and the dependent variables, and the parameter vectors of the model are assumed to be sampled from a multivariate normal distribution. The mean vector and the covariance matrix of the parameter distribution can be assumed and such a parameter distribution is referred to as the hypothetical underlying distribution. A new framework is proposed, namely, the distribution-guided heuristic search framework, which uses the information of the hypothetical underlying distribution with the following two main concepts: (i) changing the coordinate of the parameter vectors via linear transformation and (ii) probabilistically filtering a parameter vector sampled by a heuristic algorithm. The framework is not a stand-alone algorithm, but it works with any heuristic algorithms to solve the target problem. The framework was tested in two simulation studies and was applied to a real example of measuring the critical dimensions of a 2-dimensional high-aspect-ratio structure of a wafer in semiconductor manufacturing. The test results show that a heuristic algorithm within the proposed framework outperforms the original heuristic algorithm as well as other existing algorithms.